多目标优化的广义Tchebycheff范数标量化

doi:10.15960/j.cnki.issn.1007-6093.2025.02.013

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (2): 175-183.doi: 10.15960/j.cnki.issn.1007-6093.2025.02.013

多目标优化的广义Tchebycheff范数标量化

夏远梅¹, 夏丹丹¹, 赵克全¹^,*()

1. 重庆师范大学数学科学学院, 重庆 401331

收稿日期:2022-02-21 出版日期:2025-06-15 发布日期:2025-06-12
通讯作者: 赵克全 E-mail:kequanz@163.com
基金资助:
国家自然科学基金(11991024);国家自然科学基金(12171063);国家自然科学基金(12101096);国家自然科学基金(11971084);重庆市高校创新研究群体项目(CXQT20014);重庆市自然科学基金面上项目(cstc2021jcyj-msxmX0280);重庆英才计划“包干制”项目(CQYC20210302270);重庆英才计划“包干制”项目(Nos. CQYC20210302270, CQYC20210309536);重庆市教委科学技术研究项目(KJQN202100521);重庆师范大学博士启动项目(20XLB028)

Generalized Tchebycheff norm scalarization in multi-objective optimization

Yuanmei XIA¹, Dandan XIA¹, Kequan ZHAO¹^,*()

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

Received:2022-02-21 Online:2025-06-15 Published:2025-06-12
Contact: Kequan ZHAO E-mail:kequanz@163.com

摘要/Abstract

摘要：

标量化方法是多目标优化问题研究的基本内容之一。本文首先对广义Tchebycheff范数的性质进行研究, 获得了其在非负象限上的严格单调性等结果。进一步, 利用广义Tchebycheff范数的这些性质研究了多目标优化问题弱有效解、有效解、严有效解和真有效解的两类标量化结果。同时也指出, 在目标函数的凸性假设下, 本文研究的标量化与加权标量化等价。

关键词: 多目标优化, 广义Tchebycheff范数, 严格单调性, 标量化, (弱, 严, 真) 有效解

Abstract:

Scalarization method is one of the basic research subjects for multi-objective optimization problems. In this paper, we first study the properties of generalized Tchebycheff norm, and obtain some strict monotonicity results on the non-negative quadrant. Furthermore, two kinds of scalarization results of weakly efficient solutions, efficient solutions, strictly efficient solutions and properly efficient solutions of multi-objective optimization problems are studied by using the properties of the generalized Tchebycheff norm. Moreover, we point out that under the assumption of convexity of the objective function, the scalarization studied in this paper is equivalent to the weighted scalarization.

Key words: multi-objective optimization, generalized Tchebycheff norm, strict monotonicity, scalarization, (weakly, strictly, properly) efficient solutions

中图分类号:

O221.6

夏远梅, 夏丹丹, 赵克全. 多目标优化的广义Tchebycheff范数标量化[J]. 运筹学学报（中英文）, 2025, 29(2): 175-183.

Yuanmei XIA, Dandan XIA, Kequan ZHAO. Generalized Tchebycheff norm scalarization in multi-objective optimization[J]. Operations Research Transactions, 2025, 29(2): 175-183.

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多目标优化的广义Tchebycheff范数标量化

Generalized Tchebycheff norm scalarization in multi-objective optimization

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